"Mates" we are, and am sure we know each other well enough that this message will be taken solely as an observation and not in way a criticism of either yourself or The Sunday Times.
I am as fallible as anybody but have checked and double-checked my solution and in the last 24 hours have asked a friend or two to check my arithmetic and so far everyone agrees that it is a correct solution. I say this in the context that when I eventually settled down to "bleed" like yourself I continually thought, although I couldn't prove it, that this problem was likely to have more than one solution and am going to put my kneck on the block and suggest that this is the case.
I am not suggesting for one minute that your and or The Sunday Time's solution is wrong but would welcome the opportunity to check it, if only to prove, assuming I am correct, that there are at least two solutions.
Might I beg your indulgence by endeavouring to prove my solution. It is a proof in reverse.
Let us assume that the watchmaker does in fact wind and set the clocks to the correct time at 15:12 on the Tuesday and returns to check them exactly 6 days ( 144 hours ) later, ie at 15:12 the following Monday. This fully satisfies the question restraints that the shop is only open weekdays from 9:30 to 5:00 and that they are both 8 day clocks.
If it now can be shown that both a clock ( A ) running 2 minutes fast and a clock ( B ) running 8 minutes slow will both be striking 8 o'clock at 15:12 on the following Monday then the case has been proven as the question does not stipulate whether or not on the watchmakers inspection this is the first occasion that this situation has arisen. Indeed it might well be possible although I haven't proved it that they did coincide in such a manner earlier but then again that could have been outwith shop hours. Indeed there is no restraint within the question as to when the watchmaker carried out his inspection other than that it was during shop hours on the following Monday.
At 15:12 on the following Monday the clocks will read as follows:
15:12 + ( 2 X 144 )mins = 15:12 + (4hrs 48mins) = 20:00
At 15:12 Clock "A" is reading 8 o'clock that evening.
15:12 - ( 8 X 144 ) mins = 15:12 - (19hrs 12mins) = 20:00
At 15:12 Clock "B" is reading 8 o'clock the previous evening
The arithmetic must be correct, because in any hour with the clocks going 2 minutes fast and 8 minutes slow respectively then they are diverging from each other by 10 minutes in any hour.
Over a period of 6 days ( 144 hours ) the clocks will therefore have diverged by 1440 minutes which is in fact 24 hours.
Please don't tell me there is a mistake in this??
Going straight off for a blood transfusion.